🧮 algebra

1. **Problem:** For each quadratic function, find the axis of symmetry and the turning point. 2. **Formula:** The axis of symmetry for a quadratic function $y = ax^2 + bx + c$ is g

1. **State the problem:** Simplify the expression $$\sqrt{108a^6}$$ by removing all perfect squares from inside the square root, assuming $$a$$ is positive. 2. **Recall the rule:**

1. Problem: Find the scale factor for a model car 12 inches long representing a 192-inch-long car. 2. Formula: Scale factor = \frac{Model\ length}{Actual\ length}

1. **State the problem:** Rewrite the expression $\left(27 \sqrt[3]{z^2}\right)^{\frac{1}{3}}$ in the form $k \cdot z^n$ where $n$ is an integer, fraction, or exact decimal. 2. **R

1. **State the problem:** Simplify the expression $\frac{1}{5} \ln 32 - \ln 2$. 2. **Recall logarithm rules:**

1. **State the problem:** Solve the system of linear equations: Top-left pair:

1. **Problem:** For the quadratic function $y = x^2 - 8x + 8$, find (a) the axis of symmetry and (b) the turning point. 2. **Formula:** The axis of symmetry for a quadratic $y = ax

1. **State the problem:** Find the domain of the function $$K(x) = \frac{9 - 8x}{x^2 - 8x - 9}$$. 2. **Recall the domain rule:** The domain of a rational function is all real numbe

1. **State the problem:** We need to find the maximum cost of each drawer pull if the total bill for a lawnmower and 15 drawer pulls is within a $400 budget.

1. The problem is to simplify the expression with negative exponents: $m^{-2} n^{-4} p^{3}$. 2. Recall the rule for negative exponents: $a^{-b} = \frac{1}{a^{b}}$ where $a \neq 0$.

1. **State the problem:** We are given the expression $(N + 3)$ and need to understand any restrictions on the variable $N$. 2. **Identify the variable and expression:** The expres

1. The problem is to express $8p^{-3}$ as a fraction without negative exponents. 2. Recall the rule for negative exponents: $a^{-n} = \frac{1}{a^n}$ where $a \neq 0$.

1. **State the problem:** We are given a table of values for $x$ and $y$: $$\begin{array}{c|ccccc}

1. **State the problem:** Given the expression $(h t u h) = 4 h u + 3 u$ and the term $(n + 3) 3$, we want to understand the restrictions on the variables. 2. **Identify the variab

1. **State the problem:** The total bill for a lawnmower and 15 drawer pulls is within a $400 budget. The lawnmower costs 325. We need to find the maximum cost of each drawer pull.

1. **State the problem:** We need to find the maximum height of the kangaroo's jump modeled by the function $h(t) = -16t^2 + 24t$. 2. **Identify the type of function:** This is a q

1. The problem asks to find the domain of the function $$g(x) = \frac{5x}{x - 5}$$. 2. The domain of a function includes all real numbers except those that make the denominator zer

1. **State the problem:** Solve for $N$ in an equation where $N$ is the unknown variable. 2. **General approach:** To solve for $N$, isolate $N$ on one side of the equation by perf

1. **State the problem:** Solve the equation $$\frac{x}{9} = \frac{7}{15}$$ for $x$. 2. **Formula and rule:** To solve for $x$ in a proportion $\frac{a}{b} = \frac{c}{d}$, cross-mu

1. The problem states: "A number decreased by 7 is at most 13." We need to write an inequality for this. 2. Let the number be $x$. "Decreased by 7" means $x - 7$.

1. **State the problem:** Pet Supply makes a profit of $5.50 per bag of natural dog food. They want to make a profit of no less than 5225. We need to find the minimum number of bag